Preheat the oven to 450°F. Wash and remove the greens from the radishes (if they are still attached). Cut the radishes into roughly uniform size. Cut the Brussels sprouts into roughly the same size as the radishes. Place all the vegetables in a large bowl.
Drizzle the olive oil over the vegetables and then sprinkle the salt and pepper over them. Toss to coat.
Pour the vegetables onto a rimmed baking sheet. Roast in the oven for 18 minutes or until the vegetables are crisp tender, and the Brussels sprouts start to brown and char a bit.
While the vegetables are roasting, place the butter in a medium size skillet. Cook the butter over medium heat, stirring constantly, until the butter fat particles just start to brown and it smells nutty. Remove from heat and continue to stir to let the residual heat continue to cook the butter until it is golden brown. Sprinkle the lemon juice over the butter and stir in.
Once the vegetables are done roasting, plate them on a shallow dish. Drizzle the lemony brown butter over the vegetables, add more salt and pepper to taste, and sprinkle some chopped radish greens over the entire dish if you have them. Serve immediately.